How to Calculate Percentage: Formulas & Examples

What Is a Percentage?

A percentage is a way of expressing a number as a fraction of 100. The word itself comes from the Latin per centum, meaning "by the hundred." When you see 25%, it simply means 25 out of every 100, or the fraction 25/100 (which simplifies to 1/4).

Percentages are everywhere in daily life: sales tax, exam scores, discounts, tips, interest rates, and statistics. Knowing how to calculate them quickly is an essential life skill.

The Basic Percentage Formula

The fundamental formula is:

Percentage = (Part / Whole) × 100

Example: You scored 42 out of 50 on a test. What is your percentage?

(42 / 50) × 100 = 84%

Common Percentage Calculations

1. What Is X% of Y?

Convert the percentage to a decimal and multiply:

X% of Y = (X / 100) × Y

Example: What is 15% of 200?

(15 / 100) × 200 = 30

2. What Percentage Is X of Y?

Percentage = (X / Y) × 100

Example: 30 is what percentage of 200?

(30 / 200) × 100 = 15%

3. Percentage Increase or Decrease

% Change = ((New - Old) / Old) × 100

Example: A product went from $80 to $100. What is the percentage increase?

((100 - 80) / 80) × 100 = 25% increase

If the result is negative, it is a percentage decrease.

4. Finding the Original Value

If an item costs $75 after a 25% discount, what was the original price?

Original = Discounted Price / (1 - Discount%)
Original = 75 / (1 - 0.25) = 75 / 0.75 = $100

Quick Mental Math Tricks

• 10% of any number: move the decimal point one place to the left. 10% of 350 = 35.
• 5%: find 10% and halve it. 5% of 350 = 17.50.
• 1%: move the decimal two places left. 1% of 350 = 3.50.
• 20%: find 10% and double it. 20% of 350 = 70.
• X% of Y = Y% of X. So 8% of 25 is the same as 25% of 8, which is 2. This trick makes many calculations easier.

Real-World Applications

• Shopping discounts: calculate how much you save during a 30% off sale.
• Taxes: figure out the tax amount on a purchase.
• Tips: quickly compute a 15% or 20% restaurant tip.
• Grades: convert raw scores to percentages.
• Finance: understand interest rates, investment returns, and inflation.

Conclusion

Percentages are one of the most practical math concepts you will use every day. Once you memorize the basic formulas and a few mental shortcuts, you can solve percentage problems in seconds. For anything more complex, try our Percentage Calculator.